发表机构
The Institute of Mathematical Sciences (IMSc); QCAR Group, The Institute of Mathematical Sciences (IMSc); Pecslab Research; Department of Physics, Ramjas College, University of Delhi; Homi Bhabha National Institute（数学科学研究所; 量子计算与算法研究组，数学科学研究所; Pecslab 研究; 德里大学拉姆贾斯学院物理系; 霍米·巴巴国家研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将金融传染建模为伊辛/QUBO系统，提出统一优化框架，涵盖最大级联失效、最优救助分配及救助敏感性度量，并验证其与退火技术兼容。
AI 中文摘要
互联金融系统容易因交叉持股和非线性传染而发生级联失效，这使得系统性风险的分析与缓解成为一个具有挑战性的计算问题。在本工作中，我们基于伊辛模型和二次无约束二元优化（QUBO）开发了一个统一的金融网络分析优化框架。从Elliott-Golub-Jackson金融网络模型出发，我们扩展均衡估值以纳入阈值引发的失效，形式化最大级联失效问题，并推导出等价的QUBO表示。随后，我们将最优救助分配问题表述为受控伊辛模型，并将由此产生的双层优化转化为一个联合QUBO，该QUBO在预算约束下同时确定均衡失效和最优干预。为了刻画单个机构的影响力，我们引入救助敏感性作为基于响应的系统性重要性度量，并开发了一种敏感性驱动的贪婪干预策略。数值模拟展示了在不同规模金融网络上的均衡估值、最坏情况级联识别、最优救助分配和敏感性分析。除优化外，伊辛表示还为分析金融传染提供了一个通用的统计力学框架，使得响应理论、蒙特卡洛方法以及为相互作用自旋系统开发的其他技术得以应用。所提出的框架为系统性风险分析建立了一种统一方法，该方法与经典退火、量子启发优化以及新兴的量子退火技术兼容。
英文摘要
Interconnected financial systems are vulnerable to cascading failures arising from cross-holdings and nonlinear contagion, making the analysis and mitigation of systemic risk a challenging computational problem. In this work, we develop a unified optimization framework for financial network analysis based on Ising models and Quadratic Unconstrained Binary Optimization (QUBO). Starting from the Elliott Golub Jackson financial network model, we extend equilibrium valuation to incorporate threshold-induced failures, formulate the Maximum Cascade Failure Problem, and derive an equivalent QUBO representation. We then formulate the Optimal Bailout Allocation Problem as a controlled Ising model and transform the resulting bi-level optimization into a single joint QUBO that simultaneously determines equilibrium failures and optimal interventions under budget constraints. To characterize the influence of individual institutions, we introduce bailout susceptibility as a response-based measure of systemic importance and develop a susceptibility-driven greedy intervention strategy. Numerical simulations demonstrate equilibrium valuation, worst-case cascade identification, optimal bailout allocation, and susceptibility analysis on financial networks of varying sizes. Beyond optimization, the Ising representation provides a general statistical-mechanical framework for analyzing financial contagion, enabling the application of response theory, Monte Carlo methods, and other techniques developed for interacting spin systems. The proposed framework establishes a unified approach for systemic risk analysis that is compatible with classical annealing, quantum-inspired optimization, and emerging quantum annealing technologies
